Alex Salmond and SNP colleague Michael Russell accepted that more people should have been made aware that 180,000 was loaned to The Gathering Ltd - the firm set up to run the centrepiece Highland clan event as part of the Homecoming celebrations last year.
The event, held in Holyrood Park, Edinburgh, collapsed with debts of about 516,000 and the loan was written off. More than 100 creditors were left out of pocket.
The loan sparked anger among opposition parties, who accused the Scottish Government of secrecy and misusing public money.
The two ministers rejected accusations that the loan was kept "secret" despite only one agency on a specially-convened steering group being made aware.
EventScotland, a national group set up to promote Scotland, should have been "instructed" to share the information with partners, the committee was told.
Mr Salmond and Mr Russell appeared before MSPs on the Scottish Parliament's Public Audit Committee, who are following up an auditors' report on the use of taxpayers' cash.
The committee has already heard from a steering group member who said he felt "let down" by not having all the information to hand.
Mr Salmond said: "We should have insisted on EventScotland informing the rest of the steering group about the loan. I think that's a perfectly fair point to make."
He added: "I would be surprised if other members of the steering group hadn't thought it a good idea because they would be as anxious as we were to secure the future of the event.
"But, nonetheless, I think it would have been proper for us to instruct EventScotland to inform the rest of the steering group.
"We didn't instruct EventScotland not to inform the steering group, incidentally."
Mr Russell, who is now education secretary, agreed with the First Minister, and said: "I think that EventScotland should have informed the steering group, with our assistance, but there was no secrecy."
During the session, Mr Russell clashed with opposition members on the committee, forcing convener Hugh Henry to try and restore order.
Lib Dem committee member Nicol Stephen said: "Mr Russell, you seem not to like the language, but is it not a simple fact that the loan was kept secret from the partners in the event - they did not know about this loan."
Mr Russell replied: "I don't want to split hairs with you. I accept the First Minister's view that it was better if EventScotland told the other members of the steering group.
"At no time was I, or any of my officials, involved in an act of secrecy."
Mr Henry also branded the loan a "secret", prompting denials from Mr Russell.
The probe has already led to clashes with high-profile witnesses, including former permanent secretary Sir John Elvidge.
He was in charge of the civil service when the event was staged - and dismissed the investigation as "all tip and no iceberg".
His evidence was called into question following appearances by Edinburgh council leaders last month.
The Gathering was hailed as the centrepiece of the year-long Homecoming programme timed to mark the 250th anniversary of the birth of Robert Burns.